Approximation of the random inertial manifold of singularly perturbed stochastic wave equations

作者：Lv, Yan; Wang, Wei^*; Roberts, A. J.

来源：Stochastics and Dynamics, 2014, 14(2): 1350018.

DOI：10.1142/S0219493713500184

• Random inertial manifold
• singularly perturbed stochastic wave equation
• Lebesgue space
• homomorphism

By applying Rohlin's result on the classification of homomorphisms of Lebesgue space, the random inertial manifold of a stochastic damped nonlinear wave equations with singular perturbation is proved to be approximated almost surely by that of a stochastic nonlinear heat equation which is driven by a new Wiener process depending on the singular perturbation parameter. This approximation can be seen as the Smolukowski-Kramers approximation as time goes to infinity. However, as time goes infinity, the approximation changes with the small parameter, which is different from the approximation on a finite time interval.

• 单位
  南京理工大学; 南京大学